Question: Given $ m \angle BOC = 4x - 2$, $ m \angle AOB = 6x - 25$, and $ m \angle AOC = 113$, find $m\angle AOB$. $O$ $A$ $C$ $B$
Answer: From the diagram, we see that together ${\angle AOB}$ and ${\angle BOC}$ form ${\angle AOC}$ , so $ {m\angle AOB} + {m\angle BOC} = {m\angle AOC}$ Substitute in the expressions that were given for each measure: $ {6x - 25} + {4x - 2} = {113}$ Combine like terms: $ 10x - 27 = 113$ Add $27$ to both sides: $ 10x = 140$ Divide both sides by $10$ to find $x$ $ x = 14$ Substitute $14$ for $x$ in the expression that was given for $m\angle AOB$ $ m\angle AOB = 6({14}) - 25$ Simplify: $ {m\angle AOB = 84 - 25}$ So ${m\angle AOB = 59}$.